scipy.linalg.toeplitz¶

scipy.linalg.toeplitz(c, r=None)[source]¶

Construct a Toeplitz matrix.

The Toeplitz matrix has constant diagonals, with c as its first column and r as its first row. If r is not given, r == conjugate(c) is assumed.

Parameters:

Parameters:	c : array_like First column of the matrix. Whatever the actual shape of c, it will be converted to a 1-D array. r : array_like, optional First row of the matrix. If None, `r = conjugate(c)` is assumed; in this case, if c[0] is real, the result is a Hermitian matrix. r[0] is ignored; the first row of the returned matrix is `[c[0], r[1:]]`. Whatever the actual shape of r, it will be converted to a 1-D array.
Returns:	A : (len(c), len(r)) ndarray The Toeplitz matrix. Dtype is the same as `(c[0] + r[0]).dtype`.

c : array_like

First column of the matrix. Whatever the actual shape of c, it will be converted to a 1-D array.

r : array_like, optional

First row of the matrix. If None, r = conjugate(c) is assumed; in this case, if c[0] is real, the result is a Hermitian matrix. r[0] is ignored; the first row of the returned matrix is [c[0], r[1:]]. Whatever the actual shape of r, it will be converted to a 1-D array.

Returns:

A : (len(c), len(r)) ndarray

The Toeplitz matrix. Dtype is the same as (c[0] + r[0]).dtype.

See also

circulant: circulant matrix
hankel: Hankel matrix
solve_toeplitz: Solve a Toeplitz system.

Notes

The behavior when c or r is a scalar, or when c is complex and r is None, was changed in version 0.8.0. The behavior in previous versions was undocumented and is no longer supported.

Examples

>>> from scipy.linalg import toeplitz
>>> toeplitz([1,2,3], [1,4,5,6])
array([[1, 4, 5, 6],
       [2, 1, 4, 5],
       [3, 2, 1, 4]])
>>> toeplitz([1.0, 2+3j, 4-1j])
array([[ 1.+0.j,  2.-3.j,  4.+1.j],
       [ 2.+3.j,  1.+0.j,  2.-3.j],
       [ 4.-1.j,  2.+3.j,  1.+0.j]])